Sorry, what is ? This is not a standard notation. It sounds like something inverse to , but:

Let c be an element of .
By the definition of , there is a so that .

Is c an element of the domain, and is d an element of the codomain of f? But the inverse of a function is in general a relation. One can think of it as a function that maps elements of the codomain into subsets of the domain. Maybe I am thinking in the wrong direction...